Going from step 1 to step 2, the person has factored out x. However, this is incorrect because there is no x to factor from the last term d.
Factoring like this is simply the distributive property in reverse. We can check if we did the factoring right by distributing the outer term x back into the inner terms
Let's multiply the outer x by each of the inner terms (a, b and d)
x times a = ax
x times b = bx
x times d = dx <--- the result should be d and not dx
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Here is the proper way to solve for x. We first need to move the d over, which is done by subtracting d from both sides. Once all of the x terms are on one side, we can finally factor out the x. Then after that we divide both sides by the quantity (a+b)
k = ax + bx + d
k - d = ax + bx + d - d
k - d = ax + bx
k - d = x(a + b)
(k - d)/(a + b) = x(a + b)/(a + b)
(k - d)/(a + b) = x
x = (k - d)/(a + b)
The final answer is
x = (k - d)/(a + b)
which can be written as
[tex]x=\frac{k-d}{a+b}[/tex]
If you choose to use the first option, then make sure you use parenthesis as shown. The parenthesis are important to make sure that you divide all of "k-d" over all of "a+b" as one big fraction.
